Elizabeth Lucas’ pop-ornamented “Clear Blue Tuesday” virtually demands that viewers admire its chutzpah, imagine its potential and overlook the inherent impossibility of the entire conceit: an autopsy of post-9/11 grief among a cross-section of singing New Yorkers. Pic might have been alternately titled “Post-Traumatic Stress Disorder: The Musical” — or, maybe, “How Reach Exceeded Grasp.” The morbid novelty of Lucas’ near-operatic elegy could attract some attention, but it’s ultimately a misfire likely to sputter when it goes out in limited release Sept. 3.

The clear blue Tuesday in question is Sept. 11, 2001, and Manhattanites are going about their business happily, until two airplanes hit the Twin Towers. Flash forward: The various characters, whom we’ve met only cursorily, are all injured, some physically, some psychically.

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Businesswoman Caroline (Jan O’Dell) is wearing an eyepatch and limping; office drone Jain (Vedant Gokhale), an Indian, is being abused by co-workers who consider anyone dark-skinned an evil Arab; middle-management lowlife Kyle (Asa Somers), the type who’d survive a nuclear blast with the brio of a cockroach, is firing a traumatized underling, whose ill-fitting suit tells us he’s been losing weight. “No one’s to blame,” Kyle sings, followed by, “You’ve dug your own grave … ” That this lyric makes no sense at all doesn’t seem to bother anyone, but at this point, the viewer is likely to be more astounded by the fact that someone is receiving a musical sacking than by what’s actually being sung.

At a time when the cinema has embraced state-of-the-art special effects as if they were life preservers, and the most hallucinatory images can be greeted with a yawn, the concept of film characters breaking into song in the middle of a dramatic story has become too fantastical for most to swallow. But helmer Lucas is working with a double handicap: characters who sing, and voices that don’t seem to match. The distancing effect is fatally distracting, and it’s impossible to appreciate either the pain the characters are feeling or the value of the music when your brain is trying so hard to synch things up.

Few of the numbers, all of which were written by cast members, are memorable, with the exception of “Reckless,” penned by Erin Hill and delivered by her character, Etta, a sci-fi soundtrack-session harpist and one of the film’s few solidly intriguing personalities. Most of the music seems to suffer from the insidious influence of “American Idol,” which demands that every pop song be an anthem, delivered as if it were grand opera, replete with Celine Dion-style chest-thumping and instant crescendos — music that’s overproduced and underconsidered. One fairly decent number, in which Caroline sings, “This is my ever after,” goes from desperate to determined to defiant in the span of about three verses. But at least the song advances the narrative; most others simply reiterate what we already know the characters are feeling.

With a couple of glaring exceptions, the performers are charming, albeit in uncharmingly written parts. But there’s no compelling throughline to the story, such as it is, save for everyone’s preoccupation with the catastrophe of 9/11 — the lesson of which was supposed to be that New Yorkers could rise from the ashes of their own despair and, while not forgetting, at least function. Preoccupation with tragedy does not a narrative make.